It might cost you the same to have a quality painter paint your floors with a quality floor epoxy or paint as it would to have the floors refinished.
Typically there's a reason why people paint floors. Usually it's because the floor was trashed beyond repair, but sometimes it's a homeowner who just couldn't be bothered.
Painting floors was popular in the 19 teens and twenties. You'll sometimes see painted floors in Victorians and craftsman bungalows. In these cases, a painted floor can look cute and period-appropriate, depending on the floor.
I bought a midcentury ranch that had one room with a painted floor. I had the entire house's hardwoods refinished and it ended up looking absolutely beautiful. I had no idea that I had a solid birch floor on my hands until after the job was done. He was also able to get the paint off and only if you look veeery closely at certain areas can you tell that it had ever been painted. It's just beautiful now.
I have another craftsman bungalow that I'm currently flipping that has painted floors. I'm still deciding what to do about them, but these floors are fir, not hardwood, the paint is likely lead-based, and the painted floor (in the bedrooms) fits the house's style. The floor refinisher said that he would not be able to salvage the floor by stripping/refinishing because it was fir, and it had a lot of small gouges in it and some water damage on one edge.
Now I'm debating whether to paint over it with a white epoxy floor paint or put engineered hardwood over the top.
So, to answer your question, whether to paint or refinish or put a layer of some other flooring (e.g. laminate or plank vinyl) on top depends on the style of the house, the condition of the wood floor, and the type of wood. If it's a modern house (e.g. 1940's or later), then it might be better to either refinish (if the floor is in good shape) or float another floor on top.